Average Error: 29.1 → 29.2
Time: 11.7s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t\right) \cdot \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}
↓
\left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t\right) \cdot \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r99459 = x;
        double r99460 = y;
        double r99461 = r99459 * r99460;
        double r99462 = z;
        double r99463 = r99461 + r99462;
        double r99464 = r99463 * r99460;
        double r99465 = 27464.7644705;
        double r99466 = r99464 + r99465;
        double r99467 = r99466 * r99460;
        double r99468 = 230661.510616;
        double r99469 = r99467 + r99468;
        double r99470 = r99469 * r99460;
        double r99471 = t;
        double r99472 = r99470 + r99471;
        double r99473 = a;
        double r99474 = r99460 + r99473;
        double r99475 = r99474 * r99460;
        double r99476 = b;
        double r99477 = r99475 + r99476;
        double r99478 = r99477 * r99460;
        double r99479 = c;
        double r99480 = r99478 + r99479;
        double r99481 = r99480 * r99460;
        double r99482 = i;
        double r99483 = r99481 + r99482;
        double r99484 = r99472 / r99483;
        return r99484;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r99485 = x;
        double r99486 = y;
        double r99487 = r99485 * r99486;
        double r99488 = z;
        double r99489 = r99487 + r99488;
        double r99490 = r99489 * r99486;
        double r99491 = 27464.7644705;
        double r99492 = r99490 + r99491;
        double r99493 = r99492 * r99486;
        double r99494 = 230661.510616;
        double r99495 = r99493 + r99494;
        double r99496 = r99495 * r99486;
        double r99497 = t;
        double r99498 = r99496 + r99497;
        double r99499 = 1.0;
        double r99500 = a;
        double r99501 = r99486 + r99500;
        double r99502 = r99501 * r99486;
        double r99503 = b;
        double r99504 = r99502 + r99503;
        double r99505 = r99504 * r99486;
        double r99506 = c;
        double r99507 = r99505 + r99506;
        double r99508 = r99507 * r99486;
        double r99509 = i;
        double r99510 = r99508 + r99509;
        double r99511 = r99499 / r99510;
        double r99512 = r99498 * r99511;
        return r99512;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Bits error versus b

Bits error versus c

Bits error versus i

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 29.1

    \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
  2. Using strategy rm

  3. Applied div-inv29.2

    \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t\right) \cdot \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}}\]

  4. Final simplification29.2

    \[\leadsto \left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t\right) \cdot \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

Reproduce

herbie shell --seed 2020001 
(FPCore (x y z t a b c i)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2"
  :precision binary64
  (/ (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))